Mean Helicity Research Articles

Efficient enumeration and visualization of helix-coil ensembles

Helix-coil models are routinely used to interpret circular dichroism data of helical peptides or predict the helicity of naturally-occurring and designed polypeptides. However, a helix-coil model contains significantly more information than mean helicity alone, as it defines the entire ensemble—the equilibrium population of every possible helix-coil configuration—for a given sequence. Many desirable quantities of this ensemble are either not obtained as ensemble averages or are not available using standard helicity-averaging calculations. Enumeration of the entire ensemble can allow calculation of a wider set of ensemble properties, but the exponential size of the configuration space typically renders this intractable. We present an algorithm that efficiently approximates the helix-coil ensemble to arbitrary accuracy by sequentially generating a list of the M highest populated configurations in descending order of population. Truncating this list of (configuration, population) pairs at a desired accuracy provides an approximating sub-ensemble. We demonstrate several uses of this approach for providing insight into helix-coil ensembles and folding mechanisms, including landscape visualization.

Cross-helicity effect onα-type dynamo in non-equilibrium turbulence

Turbulence is typically not in equilibrium, i.e. mean quantities such as the mean energy and helicity are typically time-dependent. The effect of non-stationarity on the turbulent hydromagnetic dynamo process is studied here with the use of the two-scale direct-interaction approximation, which allows one to explicitly relate the mean turbulent Reynolds and Maxwell stresses and the mean electromotive force to the spectral characteristics of turbulence, such as the mean energy, as well as kinetic and cross-helicity. It is demonstrated that the non-equilibrium effects can enhance the dynamo process when the magnetohydrodynamic turbulence is both helical and cross-helical. This effect is based on the turbulent infinitesimal-impulse cross-response functions, which do not affect turbulent flows in equilibrium. The evolution and sources of the cross-helicity in magnetohydrodynamic turbulence are also discussed.

Broken Mirror Symmetry of Tracer's Trajectories in Turbulence.

Topological properties of physical systems play a crucial role in our understanding of nature, yet their experimental determination remains elusive. We show that the mean helicity, a dynamical invariant in ideal flows, quantitatively affects trajectories of fluid elements: the linking number of Lagrangian trajectories depends on the mean helicity. Thus, a global topological invariant and a topological number of fluid trajectories become related, and we provide an empirical expression linking them. The relation shows the existence of long-term memory in the trajectories: the links can be made of the trajectory up to a given time, with particles positions in the past. This property also allows experimental measurements of mean helicity.

Spontaneous generation and reversal of helicity in anisotropic turbulence.

Helicity plays an important role in spectacular geophysical phenomena such as hurricanes or the generation of the terrestrial magnetic field. The present investigation shows how helicity can be created in a statistically homogeneous but anisotropic flow, driven by buoyancy. If the flow is close enough to a two-dimensional limit, spontaneous symmetry breaking leads to the generation of mean helicity. In particular, we explain these observations by identifying a simple linear mechanism, the relevance of which is illustrated by simulations of unstably stratified turbulence in a conducting fluid on which a magnetic field is imposed. Finally it is shown that the self-organized state displays dynamical reversals of the sign of the mean helicity.

Constant-energetics control-based forcing methods in isotropic helical turbulence

A deterministic forcing method and stochastic forcing method are proposed to keep mean turbulence kinetic energy and mean helicity at ideal values. Using the proposed forcing methods, it is shown that characteristics common to energy and helicity dissipation rates, and results of direct numerical simulations, support the joint cascade scenario of energy and helicity.

Evolution of Magnetic Helicity in Solar Cycle 24

Abstract We propose a novel approach to reconstruct the surface magnetic helicity density on the Sun or Sun-like stars. The magnetic vector potential is determined via decomposition of vector magnetic-field measurements into toroidal and poloidal components. The method is verified using data from a non-axisymmetric dynamo model. We apply the method to vector field synoptic maps from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory to study the evolution of the magnetic helicity density during solar cycle 24. It is found that the mean helicity density of the non-axisymmetric magnetic field of the Sun evolves in a way similar to that reported for the current helicity density of the solar active regions. It predominantly has a negative sign in the northern hemisphere, while it is mainly positive in the southern hemisphere. Also, the hemispheric helicity rule for the non-axisymmetric magnetic field showed the sign inversion at the end of cycle 24. The evolution of the magnetic helicity density of a large-scale axisymmetric magnetic field is different from what is predicted by dynamo theory. On one hand, the mean large- and small-scale components of magnetic helicity density display the hemispheric helicity rule of opposite signs at the beginning of cycle 24. However, later in the cycle, the two helicities exhibit the same sign, in contrast with theoretical expectations.

The Effect of Helicity on Kinetic Energy Cascade in Compressible Helical Turbulence

Helicity plays an important role in the nonlinear dynamic process of compressible helical turbulence. We carry out direct numerical simulations (DNS) of compressible helical turbulence with different mean helicity at the grid resolution of 512(3) and try to explore the physical mechanism of kinetic energy cascade under the effect of helicity. The filtering method of coarse-graining is employed for scale decomposition to get kinetic energy flux. We get some novel conclusions in contrast to pre-existing knowledge in incompressible helical turbulence. Firstly, helicity also hinders the process of compressible kinetic energy cascade and reduces viscous dissipation. Secondly, helicity weakens some exclusive features, such as coupling between compressible and solenoidal mode of fluctuating velocity, energy transformation between kinetic energy and internal energy, and shocklets which appear only in compressible turbulence and serves as the role of constraint.

The nature of triad interactions in active turbulence

Generalised Navier–Stokes (GNS) equations describing three-dimensional active fluids with flow-dependent narrow spectral forcing have been shown to possess numerical solutions that can sustain significant energy transfer to larger scales by realising chiral Beltrami-type chaotic flows. To rationalise these findings, we study here the triad truncations of polynomial and Gaussian GNS models focusing on modes lying in the energy injection range. Identifying a previously unknown cubic invariant for the triads, we show that their asymptotic dynamics reduces to that of a forced rigid body coupled to a particle moving in a magnetic field. This analogy allows us to classify triadic interactions by their asymptotic stability: unstable triads correspond to rigid-body forcing along the largest and smallest principal axes, whereas stable triads arise from forcing along the middle axis. Analysis of the polynomial GNS model reveals that unstable triads induce exponential growth of energy and helicity, whereas stable triads develop a limit cycle of bounded energy and helicity. This suggests that the unstable triads dominate the initial relaxation stage of the full hydrodynamic equations, whereas the stable triads determine the statistically stationary state. To test whether this hypothesis extends beyond polynomial dispersion relations, we introduce and investigate an alternative Gaussian active turbulence model. Similar to the polynomial case, the steady-state chaotic flows in the Gaussian model spontaneously accumulate non-zero mean helicity while exhibiting Beltrami statistics and upward energy transport. Our results suggest that self-sustained Beltrami-type flows and an inverse energy cascade may arise generically in the presence of flow-dependent narrow spectral forcing.

Haemodynamic performance of AFX and Nellix endografts: a computational fluid dynamics study.

The objective of this study is to analyse the flow conditions in the AFX and Nellix endografts (EGs) accounting for their postimplantation configuration in patients with an endovascular aneurysm repair-treated abdominal aortic aneurysm. We reconstructed post-endovascular aneurysm repair computed tomography scans of patients treated with an AFX or Nellix EG creating post-implantation EG models. We examined 16 patients, 8 in each group. The blood flow properties were obtained by computational fluid dynamics simulations and were subsequently compared with physiological infrarenal blood flow properties measured in 5 healthy subjects. Specifically, pressure drop, maximum velocity and wall shear stress were measured at peak systole and mean helicity at mid-diastole. Our statistical analyses showed that the haemodynamic properties in both control regions did not vary statistically after the implantation of either the AFX or the Nellix EG, except for helicity that was significantly lower in the abdominal part of the Nellix EG compared with the expected physiological measurement. Regardless of the overall blood flow restoration, it is important to note that low pressure drop was detected along the limbs of the AFX and suppressed blood helical motion was detected at the entrance of the Nellix device. It is observed from the results that the AFX EG has achieved absolute restoration of blood flow after endovascular aneurysm repair, although the development of secondary flow in the upper part of the EG and the low pressure drop in its limbs should be acknowledged. The Nellix EG also seems to be haemodynamically efficient. However, the suppression of helical flow before blood enters the device might raise concerns about its clinical application.

Dynamics of helicity in homogeneous skew-isotropic turbulence

The dynamics of helicity in homogeneous skew-isotropic freely decaying turbulence is investigated, at very high Reynolds numbers, thanks to a classical eddy-damped quasi-normal Markovian (EDQNM) closure. In agreement with previous direct numerical simulations, a $k^{-5/3}$ inertial range is obtained for both the kinetic energy and helical spectra. In the early stage of the decay, when kinetic energy, initially only present at large scales cascades towards small scales, it is found that helicity slightly slows down the nonlinear transfers. Then, when the turbulence is fully developed, theoretical decay exponents are derived and assessed numerically for helicity. Furthermore, it is found that the presence of helicity does not modify the decay rate of the kinetic energy with respect to purely isotropic turbulence, except in Batchelor turbulence where the kinetic energy decays slightly more rapidly. In this case, non-local expansions are used to show analytically that the permanence of the large eddies hypothesis is verified for the helical spectrum, unlike the kinetic energy one. Moreover, the $4/3$ law for the two-point helical structure function is assessed numerically at very large Reynolds numbers. Afterwards, the evolution equation of the helicity dissipation rate is investigated analytically, which provides significant simplifications and leads notably to the definition of a helical derivative skewness and of a helical Taylor scale, which is numerically very close to the classical Taylor longitudinal scale at large Reynolds numbers. Finally, when both a mean scalar gradient and helicity are combined, the quadrature spectrum, linked to the antisymmetric part of the scalar flux, appears and scales like $k^{-7/3}$ and then like $k^{-5/3}$ in the inertial range.

Nonlinear development of the ekman layer structures

The nonlinear modes of coherent structure development in the Atmospheric boundary layer are investigated. Two-scale model of Atmospheric boundary layer is used in the calculation. The velocity field splits into large-scale profile of horizontal wind velocity and three-scale velocity field. The former depends only on the vertical coordinate. The latter is connected with roll circulation and is subject to the vertical coordinate and the coordinate perpendicular to the roll direction. The influence of turbulence is parameterized by turbulent viscosity. The modification of wind profile by rolls is taken into account. Depending on the Reynolds number, different types of the hydrodynamic instabilities specific to the Atmospheric boundary layer occurred. This appears at the relative orientation of the arising geostrophic wind and roll circulation, and also at the scales and space periods of the structures. As the Reynolds number grows, the mean energy and helicity increase. Within the range of the Reynolds number between 200÷300 the dependence is close to linear, which points to the possibility of utilizing weakly nonlinear theory methods, where perturbation amplitudes increase as Re1/2. The rise of the roll asymmetry followed by remarkable growing of the extreme amplitude of a longitudinal velocity component in the direction opposite to geostrophic wind compared to the amplitudes along the lines of geostrophic wind is detected. Increase of the positive component of helicity by contrast to the negative ones is observed simultaneously. A qualitative comparison between the modeling findings and the measured characteristics of the coherent structures observed in the Atmospheric boundary layer is carried out. In July 2007, these structures were measured by acoustic sounding methods in Kalmykia, where asymmetry in the distribution of longitudinal velocity component was observed as well. An apparent pattern of roll circulation begins to reproduce in the mesoscale atmospheric model RAMS under grid size about 500 meters. Reasonably good correspondence between simulation findings and observable vortex with centers lying about 1200÷1300 meters high is received. The values of turbulent viscosity and effective Reynolds number are typical for unstable stratification conditions.

Two-phase slug flows in helical pipes: Slug frequency alterations and helicity fluctuations

Air-water numerical simulations in the slug flow regime have been performed in horizontal helical pipes and the effects of geometries on the flow regime have been investigated. Depending on the length of the helix, outlet slug frequencies have been reduced with various degrees of efficiency. Correlations between mean tangential velocity and helicity density fluctuations have been identified and investigated qualitatively. These flow fields show smaller time scales than those obtained in volume fractions fluctuations. Shifts observed in the tangential velocity and mean helicity fluctuations to smaller time scales (high frequencies) are associated with regime transitions. For a slug flow undergoing a continuous transition to the annular flow regime, it is shown that the presence of slower (low frequencies) helicity fluctuations is attributed to the variations in the axial velocity. Finally, the analysis of the helicity at gas-liquid interface confirms the presence of the mixing zone at the slug front.

Helicity in the Ekman boundary layer

AbstractHelicity, which is defined as the scalar product of velocity and vorticity, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathcal{H}} = {\boldsymbol {u}} \boldsymbol {\cdot }\boldsymbol{\omega}$, is an inviscidly conserved quantity in a barotropic fluid. Mean helicity is zero in flows that are parity invariant. System rotation breaks parity invariance and has therefore the potential of giving rise to non-zero mean helicity. In this paper we study the helicity dynamics in the incompressible Ekman boundary layer. Evolution equations for the mean field helicity and the mean turbulent helicity are derived and it is shown that pressure flux injects helicity at a rate $ 2 \varOmega G^2 $ over the total depth of the Ekman layer, where $ G $ is the geostrophic wind far from the wall and $ {\boldsymbol{\Omega}} = \varOmega {\boldsymbol {e}}_y $ is the rotation vector and $ {\boldsymbol {e}}_y $ is the wall-normal unit vector. Thus right-handed/left-handed helicity will be injected if $ \varOmega $ is positive/negative. We also show that in the uppermost part of the boundary layer there is a net helicity injection with opposite sign as compared with the totally integrated injection. Isotropic relations for the helicity dissipation and the helicity spectrum are derived and it is shown that it is sufficient to measure two transverse velocity components and use Taylor’s hypothesis in the mean flow direction in order to measure the isotropic helicity spectrum. We compare the theoretical predictions with a direct numerical simulation of an Ekman boundary layer and confirm that there is a preference for right-handed helicity in the lower part of the Ekman layer and left-handed helicity in the uppermost part when $ \varOmega > 0 $. In the logarithmic range, the helicity dissipation conforms to isotropic relations. On the other hand, spectra show significant departures from isotropic conditions, suggesting that the Reynolds number considered in the study is not sufficiently large for isotropy to be valid in a wide range of scales. Our analytical and numerical results strongly suggest that there is a turbulent helicity cascade of right-handed helicity in the logarithmic range of the atmospheric boundary layer when $\varOmega >0$, consistent with recent measurements by Koprov, Koprov, Ponomarev & Chkhetiani (Dokl. Phys., vol. 50, 2005, pp. 419–422). The isotropic relations which are derived may facilitate future measurements of the helicity spectrum in the atmospheric boundary layer as well as in controlled wind tunnel experiments.

4D flow magnetic resonance imaging in bicuspid aortic valve disease demonstrates altered distribution of aortic blood flow helicity

Changes in aortic geometry or presence of aortic valve (AoV) disease can result in substantially altered aortic hemodynamics. Dilatation of the ascending aorta or AoV abnormalities can result in an increase in helical flow. 4D flow magnetic resonance imaging was used to test the feasibility of quantitative helicity analysis using equidistantly distributed 2D planes along the entire aorta. The evaluation of the method included three parts: (1) the quantification of helicity in 12 healthy subjects, (2) an evaluation of observer variability and test-retest reliability, and (3) the quantification of helical flow in 16 patients with congenitally altered bicuspid AoVs. Helicity quantification in healthy subjects revealed consistent directions of flow rotation along the entire aorta with high clockwise helicity in the aortic arch and an opposite rotation sense in the ascending and descending aorta. The results demonstrated good scan-rescan and inter- and intraobserver agreement of the helicity parameters. Helicity quantification in patients revealed a significant increase in absolute peak relative helicity during systole and a considerably greater heterogeneous distribution of mean helicity in the aorta. The method has the potential to serve as a reference distribution for comparisons of helical flow between healthy subjects and patients or between different patient groups.

Native State Conformational Heterogeneity of HP35 Revealed by Time-Resolved FRET

The villin headpiece subdomain (HP35) has become one of the most widely used model systems in protein folding studies, due to its small size and ultrafast folding kinetics. Here, we use HP35 as a test bed to show that the fluorescence decay kinetics of an unnatural amino acid, p-cyanophenylalanine (Phe(CN)), which are modulated by a nearby quencher (e.g., tryptophan or 7-azatryptophan) through the mechanism of fluorescence resonance energy transfer (FRET), can be used to detect protein conformational heterogeneity. This method is based on the notion that protein conformations having different donor-acceptor distances and interconverting slowly compared to the fluorescence lifetime of the donor (Phe(CN)) would exhibit different donor fluorescence lifetimes. Our results provide strong evidence suggesting that the native free energy basin of HP35 is populated with conformations that differ mostly in the position and mean helicity of the C-terminal helix. This finding is consistent with several previous experimental and computational studies. Moreover, this result holds strong implications for computational investigation of the folding mechanism of HP35.

The flow helicity in quasi-orderedcellular convection

AbstractThe helicity of cellular convective flows in a horizontal layer of compressible fluid (gas) heated from below and rotating about a vertical axis is studied using finite-difference numerical simulations. The medium is assumed to be polytropically stratified. An initial thermal perturbation is introduced so as to produce a system of Bénard-type hexagonal convection cells. The flow gradually becomes less ordered, and the mean helicity grows initially and decreases sharply after the substantial chaotisation of the flow. Given the Rayleigh and Prandtl numbers, the maximum value reached by the mean helicity increases with the decrease of the polytrope index and has a maximum at a certain rotational velocity of the layer.

The elemental shear dynamo

AbstractA quasi-linear theory is presented for how randomly forced, barotropic velocity fluctuations cause an exponentially growing, large-scale (mean) magnetic dynamo in the presence of a uniform parallel shear flow. It is a ‘kinematic’ theory for the growth of the mean magnetic energy from a small initial seed, neglecting the saturation effects of the Lorentz force. The quasi-linear approximation is most broadly justifiable by its correspondence with computational solutions of nonlinear magnetohydrodynamics, and it is rigorously derived in the limit of small magnetic Reynolds number, ${\mathit{Re}}_{\eta } \ll 1$. Dynamo action occurs even without mean helicity in the forcing or flow, but random helicity variance is then essential. In a sufficiently large domain and with a small seed wavenumber in the direction perpendicular to the mean shearing plane, a positive exponential growth rate $\gamma $ can occur for arbitrary values of ${\mathit{Re}}_{\eta } $, viscous Reynolds number ${\mathit{Re}}_{\nu } $, and random-force correlation time ${t}_{f} $ and orientation angle ${\theta }_{f} $ in the shearing plane. The value of $\gamma $ is independent of the domain size. The shear dynamo is ‘fast’, with finite $\gamma \gt 0$ in the limit of ${\mathit{Re}}_{\eta } \gg 1$. Averaged over random realizations of the forcing history, the ensemble-mean magnetic field grows more slowly, if at all, compared to the r.m.s. field (magnetic energy). In the limit of small ${\mathit{Re}}_{\eta } $ and ${\mathit{Re}}_{\nu } $, the dynamo behaviour is related to the well-known alpha–omega ansatz when the force is slowly varying ($\gamma {t}_{f} \gg 1$) and to the ‘incoherent’ alpha–omega ansatz when the force is more rapidly fluctuating.

Helical scenario of tropical cyclone genesis and intensification

A helical scenario of tropical cyclogenesis and further vortex intensification is proposed based on results of direct numerical simulation of atmospheric flows. The main idea of the scenario consists in a specific topology of helical flows which are characterized by the linkage of vortex lines. Velocity fields resulting from a high resolution numerical simulation by the Regional Atmospheric Modeling System (RAMS) are used to calculate helical and integral characteristics during a tropical cyclone formation. It is shown how non-zero mean helicity is generated by moist convective atmospheric turbulence, which implies a new flow topology with linked vortex lines. A possible role of vortical hot towers (VHTs) is discussed in generating the linkage. It is shown that the linkage results in a positive feedback between the horizontal and vertical circulation in the formation of a larger-scale vortex and contributes to the instability of the macro vortex.

The dynamics of two interacting compositional plumes in the presence of a magnetic field

The dynamics of two compositionally buoyant columns of fluid rising in an infinite less buoyant fluid is studied in the presence of a uniform magnetic field, B 0. The fluid is thermally stably stratified and has a viscosity, ν, a thermal diffusivity, κ and magnetic diffusivity, η. The stability of the mean state to infinitesimal disturbances is governed by the seven dimensionless parameters: the Reynolds number, R (=UL/ν, where U, L are characteristic velocity and length respectively) which measures the strength of the compositional buoyancy; the dimensionless measures x 0, x 1, d of the thickness of the two plumes and the distance between them, respectively; the ratio Γ of the strengths of the two plumes (as measured by their basic concentration of light material); the Chandrasekhar number, Qc (=, in which μ is the magnetic permeability, ρ0 the fluid density and B 0 a characteristic unit of magnetic field), is a measure of the magnitude of the magnetic field and the normalized horizontal projection of the magnetic field, where θ measures the inclination of the magnetic field to the vertical. The stability is examined for small values of R. The preferred mode of instability is studied in the parameter space (x 0, x 1, d, ). It is shown that the influence of the magnetic field does not change the order of the magnitude of the growth rate from O(R 0) of the two non-magnetic interacting plumes and it does not introduce any new modes to the stability problem. However, the presence of the magnetic field introduces novel features to the stability problem. For any fixed set x 0, x 1, d, Γ, Qc, the growth rate can either increase with or initially decrease reaching a minimum before it increases again. As Qc increases, with fixed, the growth rate can assume one of four different behaviours: (i) it maintains the same value of the non-magnetic case with the disturbance propagating along field lines; (ii) it decreases steadily with Qc; (iii) it maintains the same value as in the absence of the field until a value is reached when it starts to increase to a maximum before it decreases to zero for large values of Qc and (iv) it increases from its value for Qc = 0 reaching a maximum before it decreases steadily to zero at some value of Qc dependent on the other parameters. The helicity and α-effect have also been studied to find that the unstable motions can produce mean helicity and α-effect.

Influence of initial mean helicity on homogeneous turbulent shear flow

Helicity statistics are studied in homogeneous turbulent shear flow. Initial mean helicity is imposed on an isotropic turbulence field using a decomposition of the flow into complex-valued helical waves. The initial decay of the turbulent kinetic energy is weakened in the presence of strong mean helicity, consistent with an analytic analysis of the spectral tensor of velocity correlations. While exponential growth of the mean turbulent kinetic energy is obtained, the mean helicity decays. Probability distribution functions (PDFs) of helicity are skewed and show that the imposed mean helicity prevails throughout the simulations. A wavelet-based scale-dependent analysis shows a trend to two dimensionalization for large scales of motion and a preference for helical motion at small scales. The magnitude of the skewness of the PDFs decreases for smaller scales. Joint PDFs indicate a strong correlation of the signs of both, helicity and superhelicity, for all cases. This correlation supports the conjecture that superhelicity dissipates helicity.